Introduction

In recent years, head-mounted displays have been widely developed for Virtual Reality (VR) simulations and video games. However, due to the need to wear stereoscopic displays, users cannot view their real environment. Traditionally, the virtual environment’s boundary does not match that of a user’s real environment. Thus, collisions between the user and the real world always occur in VR applications and cause poor user experiences.

To create an adaptive virtual environment, boundary measurement of the real environment is necessary for warnings. Currently, a light detection and ranging (LiDAR) sensor is utilised to detect the 3D point cloud of the surrounding environment. From the point cloud, large planar regions are recognised as the boundary walls [1]. In order to detect the boundary of an indoor environment, this paper develops a boundary wall detection method based on the Hough transform algorithm [2]. After the Hough transform is implemented on the LiDAR datasets, a connected-component-labelling (CCL) algorithm is applied to classify the segmented intensive regions of the Hough space into several distinguishable blocks. The corresponding Hough coordinates of the largest four peaks of the blocks are recognised as the wall plane parameters. By scaling the virtual environment to the real environmental range, the user is able to act in the virtual environment without collisions, thus enhancing the user experience.

The tracking of the skeleton of a human body using RGB images and the depth sensors of the Microsoft Kinect has been widely applied for interactions between users and virtual objects in VR applications [3]. When we utilise the Kinect to acquire a user’s gesture, the user needs to stand in front of the Kinect within a limited distance and face the Kinect [4]. Otherwise, weak and inaccurate signals are sensed. For omnidirectional detection, this paper proposes a multiple Kinect network using a bivariate Gaussian probability density function (PDF). In the system, multiple Kinect sensors installed in an indoor environment detect a user’s gesture information from different viewpoints. The sensed datasets of the distributed clients are sent to a VR management server that selects an adaptive Kinect based on the user’s distance and orientation. In our method, only small datasets of the user’s position and body joints are delivered from the Kinect clients to the server; this satisfies the real-time transmission requirements [5].

The remainder of this paper is organised as follows. “Related works” section provides an overview of related works. “A 3D localisation system” section describes the 3D localisation system, including the environmental boundary walls detection method and wireless Kinect sensor network selection. “Experiments” section illustrates the experiment results. Finally, “Conclusions” section concludes this paper.

Related works

To realise a virtual–physical collaboration approach, environmental recognition methods such as plane and feature detection have been researched [6]. Zucchelli et al. [7] detected planes from stereo images using a motion-based segmentation algorithm. The planar parameters were extracted automatically with projective distortions. The traditional Hough transform was usually used to detect straight lines and geometric shapes from the images. Trucco et al. [8] detected the planes from the disparity space using a Hough-like algorithm. Using these methods, matching errors were caused when the outliers overlapped with the plane regions.

To detect continuous planes, Hulik et al. [9] optimised a 3D Hough transform to extract large planes from LiDAR and Kinect RGB-D datasets. Using a Gaussian smoothing function, the noise in the Hough space was removed to preserve the accuracy of the plane detection process. In order to speed up the Hough space updating process, a caching technique was applied for point registration. Compared with the traditional plane detection algorithm Compared Random sample consensus (RANSAC) [10], the 3D Hough transform performed faster and was more stable. During the maxima extraction process from the Hough space, this method applied a sliding window technique with a pre-computed Gaussian kernel. When dense noise exists surrounding a line, more than one peak is extracted in a connected segmented region using this method. In order to maintain stable line estimation, this paper applied a CCL algorithm to preserve only one peak extracted in one distinguishable region [11].

To localise and recognise a user’s motion, Kinect is a popular display device in VR development. It is able to report on the user’s localisation and gesture information. However, a single Kinect can only capture the front-side of users facing the sensor. To sense the back-side, Chen et al. [12] utilised multiple Kinects to reconstruct an entire 3D mesh of the segmented foreground human voxels with colour information. To track people in unconstrained environments, Sun et al. [13] proposed a pairwise skeleton matching scheme using the sensing results from multiple Kinects. Using a Kalman filter, their skeleton joints were calibrated and tracked across consecutive frames. Using this method, we found that different Kinects provided different localisation of joints because the sensed surfaces were not the same from different viewpoints.

To acquire accurate datasets from multiple sensors, Chua et al. [14] addressed a sensor selection problem in a smart-house using a naïve Bayes classifier, a decision tree and k-Nearest-Neighbour algorithms. Sevrin et al. [15] proposed a people localisation system with a multiple Kinects trajectory fusion algorithm. The system adaptively selected the best possible choice among the Kinects in order to detect people with a highly accurate rate [16]. Following these sensor selection methods, we developed a wireless and reliable sensor network for VR applications to enable users to walk and interact freely with virtual objects.

A 3D localisation system

This section describes an indoor 3D localisation system for VR applications. A Hough transform algorithm is applied to detect the indoor boundary walls. A multiple Kinects selection method is proposed to localise a user’s position with an omnidirectional orientation.

Indoor boundary detection from 3D point clouds

To estimate the localisation of indoor walls, we describe a framework of plane detection in 3D point clouds, as shown in Fig. 1. The framework mainly includes the registration of 3D point clouds, a height histogram of 3D points, non-ground points segmentation and planar surface detection.

Fig. 1
figure 1

A framework for planar detection using 3D point clouds

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An indoor environment always contains six large planes, including four surrounding walls, the floor and the roof. This project aims to segment the non-ground walls from the detected planes to estimate the environmental size. A height histogram, as shown in Fig. 2, is first utilised to estimate the voxel distribution of the height [14]. Since the points located on the floor or roof surfaces always have the same height value, the two peaks of the height histogram are considered to be the floor and roof surfaces. After the peaks are filtered out, the non-ground points are then segmented.

Fig. 2
figure 2

The proposed height histogram

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In indoor environments, the planes of boundary walls always form a cuboid shape. Since most LiDAR points are projected onto the walls, the mapped 2D points on the x–z plane from the wall points are combined into four straight lines. The pairwise opposite lines are parallel to each other and the neighbour lines are orthogonal to each other. For indoor boundary detection, a Hough transform algorithm is applied to estimate the parameters of the mapped lines on x–z plane from the segmented non-ground voxels. A flowchart of the applied Hough Transform is shown in Fig. 3.

Fig. 3
figure 3

A flowchart of the applied Hough Transform

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We assume that the walls are always orthogonal to the x–z plane. Hence, the wall plane is formulated using the following linear Eq. (1):

$$r = x\cos \alpha + z\sin \alpha$$
(1)

As shown in Fig. 4a, r is the distance from the origin to the straight line and α is the angle between the vertical direction of the line with the x axis. The Hough space is defined as the (r–α) plane calculated from a set of LiDAR points in x and z coordinates. The approximate sinusoidal curve in Fig. 4b represents the Hough space of a 2D point. As shown in Fig. 4c, all sinusoidal curves computed using the Hough transform from the points in a straight line cross at several points. The r and α coordinates of the maxima in the Hough space are the line parameters.

Fig. 4
figure 4

An illustration of the Hough Transform. a Line parameters r and α. b The r–α plot of a 2D point. c The r–α plot of a line. d The r–α plot of all x–z coordinates

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The wall planes contain most of the points that form several straight lines on the x–z plane. Therefore, the four peaks of the Hough space are recognised as the parameters of the boundary wall planes after the (r, α) coordinates are generated from all the sensed indoor points using the Hough Transform. Each (r, α) cell in the Hough space records the count of the mapped LiDAR points; these indicate the occurrence frequency. The four peaks always exist in the intensive areas as shown in Fig. 4d.

Figure 5a presents an instance of the occurrence frequency in the Hough space. To segment the intensive areas, the low frequency cells are filtered out using a threshold based on the occurrence frequency distribution of the cells. The valid cells are segmented as shown in Fig. 5b, and are classified into several distinguishable blocks using the CCL algorithm. In the CCL algorithm, the label of each cell is initialised corresponding to its index, as shown in Fig. 5c. To mark each distinguishable block with a unique label, the minimum label in Fig. 5d is searched for among a clique of each cell that contains the local, right and bottom cells. The clique updates the labels with the minimum label in it. Several seeking iterations of the minimum labels are implemented until all labels remain unchanged. The minimum label in a distinguishable block in Fig. 5e is the indicator of the connected valid cells. Finally, the corresponding (r, α) coordinate of the largest value in each distinguishable block of Fig. 5f is the required straight-line parameter.

Fig. 5
figure 5

The process of the CCL algorithm. a The counts of the occurrence frequency in the Hough space. b The valid cells segmented using a threshold. c The labels initialised corresponding to the cell indices. d The process of finding the minimum labels among each clique. e The minimum labelling result. f Peak extraction of each distinguishable cluster

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Adaptive Kinect selection

We propose a wireless sensor network to localise the VR user using the integration of multiple Kinects. As shown in Fig. 6, the user’s motion and position datasets are detected from multiple views using the Kinects. The distributed Kinects report the sensed datasets to a VR server via a WiFi network. An adaptive Kinect is selected using a bivariate Gaussian PDF.

Fig. 6
figure 6

The proposed 3D localisation method using multiple Kinects

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A Kinect is installed at each client to detect the user’s gesture information from different viewpoints. From several gathered datasets, the effectiveness of each sensor is generated based on the user’s distance d i and orientation θ i to the Kinect k i . If the distance is close and the orientation of the user is facing towards a sensor, the effectiveness of this sensor is then high. To select the best sensor, we apply a bivariate Gaussian PDF for the effectiveness estimation, formulated as follows:

$$f_{k_{i}} (d_{i} ,\theta_{i} ) = \frac{{\exp \left[ { - \frac{{\left(\frac{{d_{i} - d_{0} }}{{\sigma_{1} }}\right)^{2} - \frac{{2\rho \left(d_{i} - d_{0} \right)\left(\theta_{i} - \theta_{0} \right)}}{{\sigma_{1} \sigma_{2} }} + \left(\frac{{\theta_{i} - \theta_{0} }}{{\sigma_{2} }}\right)^{2} }}{{2\left(1 - \rho^{2} \right)}}} \right]}}{{2\pi \sigma_{1} \sigma_{2} \sqrt {1 - \rho^{2} } }} .$$
(2)

Here, the variables d∈[0 ~ ∞), θ∈[− π~π), σ 1 = 1, σ 2 = 1, ρ∈[− 1, 0]. The adaptive Kinect is selected using a maximum likelihood function expressed as follows:

$$k = \mathop {\arg \hbox{max} }\limits_{{k_{i} }} f_{{k_{i} }} (d_{i} ,\theta_{i} ) .$$
(3)

Experiments

In this section, we analyse the performance of the proposed indoor boundary walls detection method from LiDAR points and illustrate a VR application developed using the proposed 3D localisation method. The experiments were implemented using one HDL-32E Velodyne LiDAR and two Microsoft Kinect2 sensors. The wall detection method was executed on a 3.20 GHz Intel® Core™ Quad CPU computer with a GeForce GT 770 graphics card and 4 GB of RAM. The Kinects were utilised to detect a user’s gesture on two clients; these were 3.1 GHz Intel® Core™ i7-5557U CPU NUC mini PCs with 16 GB of RAM. The VR client was implemented on a Samsung Gear VR with a Samsung Galaxy Note 4 in it. The Note 4 had a 2.7 GHz Qualcomm Snapdragon Quad CPU, 3 GB of RAM, a 2560 × 1440 pixels resolution and the Android 4.4 operating system.

The applied HDL-32E was able to sense 32 × 12 3D points in a packet per 552.96 μs. The field of view was 41.34° in the vertical direction and 360° in the horizontal direction with an angular resolution of 1.33°. The valid range was 70 m with an error variance of 2 cm. In our project, the 3D point clouds were reconstructed using DirectX software development kits. Figure 7a presents the raw datasets of 180 × 32 × 12 points sensed by a stationary Velodyne LiDAR in an indoor environment. By projecting the non-ground points onto the x–z plane, a density diagram was generated as shown in Fig. 7b where mapped cells with a high density are represented using red. The intensive regions of line shapes were considered to be the boundary walls.

Fig. 7
figure 7

A 3D representation scene of the LiDAR datasets. a The 180 raw datasets of the 3D point cloud. b The x–z coordinates projected from non-ground points

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Using the proposed Hough Transform, the Hough space shown in Fig. 8a was generated from the non-ground points. The brightness of a cell in the Hough space indicates the occupied frequency of the (r, α) coordinates. In our experiment, the range of the distance r was calculated to be between − 10.598 and 5.909 m and the inclination angle α was between 0° and 180°. The system allocated an 825 × 360 integer buffer for the Hough space cache. Using a threshold computed based on the value distribution of the Hough space, the intensive regions were segmented as shown in Fig. 8b. After the proposed CCL algorithm was implemented using 19 iterations, 55 distinguishable blocks were grouped using different colours as shown in Fig. 9c. By selecting the four largest peaks from the distinguishable blocks, the corresponding coordinates (r, α) were calculated using the parameters of the straight lines. In Fig. 9d, we displayed the detected boundary walls with the LiDAR points. The estimated wall planes are located on the wall voxels, thus proving that our proposed method was accurate.

Fig. 8
figure 8

The experimental results of indoor boundary detection from 3D point clouds. a The Hough space generated from the projected x–z coordinates using a Hough Transform. b The intensive areas filtered using a threshold. c The distinguishable blocks grouped using the CCL algorithm. d A representation of the detected boundary walls from the LiDAR points

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Fig. 9
figure 9

A VR boxing game developed using the proposed wireless multiple Kinect sensors selection system

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The range of the indoor environment was estimated to be 9.94 m in length and 7.54 m in width. The virtual environment was resized to correspond to the real environment so as to achieve virtual–physical synchronisation. The wall detection method was implemented during an initialisation step before the VR application was started. Using the proposed system, we developed a VR boxing game as shown in Fig. 9.

In the system, the user’s location and orientation were detected by two Kinects. When the player was facing a Kinect with a distance between 2 and 6 m, the motion information was sensed precisely. Through the experiments, we found that d 0 = 5.0 and θ 0 = 0.0 is the perfect position for Kinect detection. Through the selection of an effective Kinect, the user was able to make free movements and interact with the virtual boxer from an omnidirectional orientation. Meanwhile, the monitor of the server rendered the game visualisation result synchronously with the VR display. The processing speed of our application including data sensing, transmission and visualisation was greater than 35 fps; this successfully achieved the real-time requirements.

Conclusions

To provide a free movement environment for VR applications, this paper demonstrated a 3D localisation method for virtual–physical synchronisation. For environmental detection, we utilised a HDL-32E Velodyne LiDAR sensor to detect the surrounding 3D point clouds. Using the Hough transform, a plane detection algorithm was proposed to extract indoor walls from point clouds so as to estimate the distance range of the surrounding environment. The virtual environment was then correspondingly resized. To match the user’s position between real and virtual worlds, a wireless Kinects network was proposed for omnidirectional detection of the user’s localisation. In the sensor selection process, we applied a Bivariate Gaussian PDF and the Maximum Likelihood Estimation method to select an adaptive Kinect. In the future, we will integrate touch sensors to the system for virtual–physical collaboration.